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Chapter Contents
Chapter Introduction
NAG Toolbox

# NAG Toolbox: nag_matop_ztfttr (f01vh)

## Purpose

nag_matop_ztfttr (f01vh) unpacks a complex triangular matrix stored in Rectangular Full Packed (RFP) format to full format in a two-dimensional array. The RFP storage format is described in Section [Rectangular Full Packed (RFP) Storage] in the F07 Chapter Introduction.

## Syntax

[a, info] = f01vh(transr, uplo, n, arf)
[a, info] = nag_matop_ztfttr(transr, uplo, n, arf)

## Description

nag_matop_ztfttr (f01vh) unpacks a complex n$n$ by n$n$ triangular matrix A$A$, stored in RFP format to conventional storage in a two-dimensional array. This function is intended for possible use in conjunction with functions from Chapter F07 where some functions that use triangular matrices store them in RFP format.

None.

## Parameters

### Compulsory Input Parameters

1:     transr – string (length ≥ 1)
Specifies whether the normal RFP representation of A$A$ or its conjugate transpose is stored.
transr = 'N'${\mathbf{transr}}=\text{'N'}$
The matrix A$A$ is stored in normal RFP format.
transr = 'C'${\mathbf{transr}}=\text{'C'}$
The conjugate transpose of the RFP representation of the matrix A$A$ is stored.
Constraint: transr = 'N'${\mathbf{transr}}=\text{'N'}$ or 'C'$\text{'C'}$.
2:     uplo – string (length ≥ 1)
Specifies whether A$A$ is upper or lower triangular.
uplo = 'U'${\mathbf{uplo}}=\text{'U'}$
A$A$ is upper triangular.
uplo = 'L'${\mathbf{uplo}}=\text{'L'}$
A$A$ is lower triangular.
Constraint: uplo = 'U'${\mathbf{uplo}}=\text{'U'}$ or 'L'$\text{'L'}$.
3:     n – int64int32nag_int scalar
n$n$, the order of the matrix A$A$.
Constraint: n0${\mathbf{n}}\ge 0$.
4:     arf(n × (n + 1) / 2${\mathbf{n}}×\left({\mathbf{n}}+1\right)/2$) – complex array
The n$n$ by n$n$ triangular matrix A$A$ in RFP format, as described in Section [Rectangular Full Packed (RFP) Storage] in the F07 Chapter Introduction.

None.

lda

### Output Parameters

1:     a(lda, : $:$) – complex array
The first dimension of the array a will be max (1,n)$\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$
The second dimension of the array will be n${\mathbf{n}}$
ldamax (1,n)$\mathit{lda}\ge \mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$.
The triangular matrix A$A$.
• If uplo = 'U'${\mathbf{uplo}}=\text{'U'}$, a$a$ is upper triangular and the elements of the array below the diagonal are not referenced.
• If uplo = 'L'${\mathbf{uplo}}=\text{'L'}$, a$a$ is lower triangular and the elements of the array above the diagonal are not referenced.
2:     info – int64int32nag_int scalar
info = 0${\mathbf{info}}=0$ unless the function detects an error (see Section [Error Indicators and Warnings]).

## Error Indicators and Warnings

info = i${\mathbf{info}}=-i$
If info = i${\mathbf{info}}=-i$, parameter i$i$ had an illegal value on entry. The parameters are numbered as follows:
1: transr, 2: uplo, 3: n, 4: arf, 5: a, 6: lda, 7: info.
It is possible that info refers to a parameter that is omitted from the MATLAB interface. This usually indicates that an error in one of the other input parameters has caused an incorrect value to be inferred.

Not applicable.

None.

## Example

```function nag_matop_ztfttr_example
transr = 'n';
uplo   = 'u';
n      = int64(4);
arf = [1.3 + 1.3i;
2.3 + 2.3i;
3.3 + 3.3i;
1.1 - 1.1i;
1.2 - 1.2i;
1.4 + 1.4i;
2.4 + 2.4i;
3.4 + 3.4i;
4.4 + 4.4i;
2.2 - 2.2i];
% Print the packed vector
fprintf('\n');
[ifail] = ...
nag_file_print_matrix_complex_gen_comp('g', 'x', arf, 'b', 'f5.2', 'RFP Packed Array arf:', 'i', ...
'n', int64(80), int64(0));
% Convert to triangular form
[a, info] = nag_matop_ztfttr(transr, uplo, n, arf);
% Print the unpacked matrix
fprintf('\n');
[ifail] = ...
nag_file_print_matrix_complex_gen_comp(uplo, 'n', a, 'b', 'f5.2', 'Unpacked matrix a:', 'i', ...
'i', int64(80), int64(0))
```
```

RFP Packed Array arf:
1  ( 1.30, 1.30)
2  ( 2.30, 2.30)
3  ( 3.30, 3.30)
4  ( 1.10,-1.10)
5  ( 1.20,-1.20)
6  ( 1.40, 1.40)
7  ( 2.40, 2.40)
8  ( 3.40, 3.40)
9  ( 4.40, 4.40)
10  ( 2.20,-2.20)

Unpacked matrix a:
1             2             3             4
1  ( 1.10, 1.10) ( 1.20, 1.20) ( 1.30, 1.30) ( 1.40, 1.40)
2                ( 2.20, 2.20) ( 2.30, 2.30) ( 2.40, 2.40)
3                              ( 3.30, 3.30) ( 3.40, 3.40)
4                                            ( 4.40, 4.40)

ifail =

0

```
```function f01vh_example
transr = 'n';
uplo   = 'u';
n      = int64(4);
arf = [1.3 + 1.3i;
2.3 + 2.3i;
3.3 + 3.3i;
1.1 - 1.1i;
1.2 - 1.2i;
1.4 + 1.4i;
2.4 + 2.4i;
3.4 + 3.4i;
4.4 + 4.4i;
2.2 - 2.2i];
% Print the packed vector
fprintf('\n');
[ifail] = x04db('g', 'x', arf, 'b', 'f5.2', 'RFP Packed Array arf:', 'i', ...
'n', int64(80), int64(0));
% Convert to triangular form
[a, info] = f01vh(transr, uplo, n, arf);
% Print the unpacked matrix
fprintf('\n');
[ifail] = x04db(uplo, 'n', a, 'b', 'f5.2', 'Unpacked matrix a:', 'i', ...
'i', int64(80), int64(0))
```
```

RFP Packed Array arf:
1  ( 1.30, 1.30)
2  ( 2.30, 2.30)
3  ( 3.30, 3.30)
4  ( 1.10,-1.10)
5  ( 1.20,-1.20)
6  ( 1.40, 1.40)
7  ( 2.40, 2.40)
8  ( 3.40, 3.40)
9  ( 4.40, 4.40)
10  ( 2.20,-2.20)

Unpacked matrix a:
1             2             3             4
1  ( 1.10, 1.10) ( 1.20, 1.20) ( 1.30, 1.30) ( 1.40, 1.40)
2                ( 2.20, 2.20) ( 2.30, 2.30) ( 2.40, 2.40)
3                              ( 3.30, 3.30) ( 3.40, 3.40)
4                                            ( 4.40, 4.40)

ifail =

0

```